The Behavior of the Gaussian Probability Density Function
Visualizes and calculates the behavior of the bivariate Gaussian probability density function
Discusses probability density and distribution, random variables, variance, and correlation
Uses surface plots, contour plots, 3D plots, numerical integration, the central limit theorem, and coordinate transformations
This PTC Mathcad worksheet walks you through an example of two random variables with joint density. It then visualizes the density function via surface and contour plots, and calculates the probability of an event.
The sample data used as an example compares the height and weight of students in a classroom to see if height and weight are positively correlated. The PDF shows you how to calculate the mean, variance, and correlation coefficient using PTC Mathcad software. It uses coordinate transformation to plot the data of interest with a constant density curve, in this case an ellipse. A description of the theory and relevant topics are discussed and equations, formulas, graphs, examples, and solutions are all provided in an instructional manner.